Improved regularity estimates for Lagrangian flows on RCD(K, N) spaces. (January 2022)

• Record Type: Journal Article
• Authors: Brué, Elia; Deng, Qin; Semola, Daniele
• Is Part Of: Nonlinear analysis. Volume 214(2022)
• Publication Date: 2022-01
• Subjects: Non smooth geometry -- Lagrangian -- Ricci curvature; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112609
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper gives a contribution to the study of regularity of Lagrangian flows on non-smooth spaces with lower Ricci curvature bounds. The main novelties with respect to the existing literature are the better behaviour with respect to time and the local nature of the regularity estimates. These are obtained by sharpening previous results of the first and third authors, in combination with some tools recently developed by the second author (adapting to the synthetic framework ideas introduced in Colding and Naber (2012)). The estimates are suitable for applications to the fine study of RCD spaces and play a central role in the construction of a parallel transport in this setting.